Robust Inference for High-Dimensional Panel Data Models

In this paper, we propose a robust estimation and inferential method for high-dimensional panel data models. Specifically, (1) we investigate the case where the number of regressors can grow faster than the sample size, (2) we pay particular attention to non-Gaussian, serially and cross-sectionally correlated and heteroskedastic error processes, and (3) we develop an estimation method for high-dimensional long-run covariance matrix using a thresholded estimator. Methodologically and technically, we develop two Nagaev-types of concentration inequalities: one for a partial sum and the other for a quadratic form, subject to a set of easily verifiable conditions. Leveraging these two inequalities, we also derive a non-asymptotic bound for the LASSO estimator, achieve asymptotic normality via the node-wise LASSO regression, and establish a sharp convergence rate for the thresholded heteroskedasticity and autocorrelation consistent (HAC) estimator. Our study thus provides the relevant literature with a complete toolkit for conducting inference about the parameters of interest involved in a high-dimensional panel data framework. We also demonstrate the practical relevance of these theoretical results by investigating a high-dimensional panel data model with interactive fixed effects. Moreover, we conduct extensive numerical studies using simulated and real data examples.